Distributed Quantum Neural Networks via Partitioned Features Encoding

Yoshiaki Kawase

arxiv: 2312.13650 · v2 · submitted 2023-12-21 · 🪐 quant-ph · cs.LG

Distributed Quantum Neural Networks via Partitioned Features Encoding

Yoshiaki Kawase This is my paper

Pith reviewed 2026-05-24 05:24 UTC · model grok-4.3

classification 🪐 quant-ph cs.LG

keywords distributed quantum neural networksfeature partitioningquantum machine learningMNIST classificationnear-term quantum devicesensemble expectation valueshandwritten digit recognitionSemeion dataset

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The pith

Splitting input features across multiple small quantum neural networks and combining their expectation values enables over 96 percent accuracy on ten-class MNIST classification while cutting hardware needs per circuit.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper proposes distributing partitioned features over several small quantum neural networks and using the ensemble of their expectation values to form predictions, rather than approximating one large circuit. This avoids the exponential number of evaluations required for large-circuit approximation. Tests on the Semeion and MNIST handwritten-digit datasets show the approach can match or exceed single-network performance. On MNIST it reaches more than 96 percent accuracy for ten classes. The method lowers the qubit and circuit-depth demands on each individual network, making the technique suitable for near-term devices.

Core claim

The authors state that partitioning the features of each input and assigning the partitions to independently trained small quantum neural networks, then forming predictions from the ensemble of those networks' expectation values, produces ten-class classification accuracy exceeding 96 percent on the MNIST dataset while requiring less hardware per network than a single large quantum neural network would need.

What carries the argument

Partitioned features encoding, which splits each input's features among separate small quantum circuits whose expectation values are then ensembled for the output.

If this is right

The method achieves high-accuracy predictions on large datasets without requiring an exponential number of small-circuit evaluations.
Each quantum neural network needs fewer qubits and shallower depth than one large network.
On the Semeion dataset performance can exceed that of a single network, but too many partitions lowers accuracy.
The approach remains compatible with the limited resources of near-term quantum hardware.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same partitioning idea could be applied to other supervised tasks where circuit size is limited by available qubits.
Varying the partition count per dataset might yield an optimal balance between accuracy and resource use.
Classical ensemble techniques could be combined with the quantum outputs to further improve robustness.
Evaluating the method on non-image data would test whether the feature-partition benefit holds beyond digit recognition.

Load-bearing premise

The ensemble of expectation values from the small circuits on partitioned features still captures enough information to distinguish the classes accurately.

What would settle it

Applying the partitioned approach to the MNIST dataset and obtaining accuracy substantially below 96 percent or below that of a comparable single larger circuit would show the ensemble fails to preserve sufficient discriminative power.

read the original abstract

Quantum neural networks are expected to be a promising application in near-term quantum computing, but face challenges such as vanishing gradients during optimization and limited expressibility by a limited number of qubits and shallow circuits. To mitigate these challenges, an approach using distributed quantum neural networks has been proposed to make a prediction by approximating outputs of a large circuit using multiple small circuits. However, the approximation of a large circuit requires an exponential number of small circuit evaluations. Here, we instead propose to distribute partitioned features over multiple small quantum neural networks and use the ensemble of their expectation values to generate predictions. To verify our distributed approach, we demonstrate ten class classification of the Semeion and MNIST handwritten digit datasets. The results of the Semeion dataset imply that while our distributed approach may outperform a single quantum neural network in classification performance, excessive partitioning reduces performance. Nevertheless, for the MNIST dataset, we succeeded in ten class classification with exceeding 96\% accuracy. Our proposed method not only achieved highly accurate predictions for a large dataset but also reduced the hardware requirements for each quantum neural network compared to a large single quantum neural network. Our results highlight distributed quantum neural networks as a promising direction for practical quantum machine learning algorithms compatible with near-term quantum devices. We hope that our approach is useful for exploring quantum machine learning applications.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

Partitioned features let small QNNs hit over 96% on MNIST 10-class but the writeup gives almost no training or baseline details.

read the letter

The one thing to know is that this paper reaches over 96% accuracy on 10-class MNIST by splitting input features across several small QNNs, training them separately, and ensembling their expectation values. This sidesteps the exponential number of evaluations needed in earlier distributed QNN approximation schemes. The work tests the idea on both Semeion and MNIST and is straightforward enough to report that excessive partitioning hurts results on Semeion. That honesty gives a sense of where the method breaks. The MNIST number shows the ensemble can keep enough signal for that dataset while cutting qubits and depth per circuit. The approach is new in its framing as a feature-partition alternative rather than a circuit-approximation one, and the empirical outcome on a standard large dataset is the concrete contribution. The soft spots sit in the missing controls. The abstract supplies no training procedure, no error bars, no direct comparison to a single large QNN or to classical baselines, and no description of how features were grouped or how many partitions were used. The stress-test point about broken inter-feature correlations is worth checking; the paper itself shows performance drops with too many partitions, so the MNIST success may depend on a specific split that is not detailed here. Nothing in the reported results looks circular or self-referential. The citations track relevant prior distributed QNN papers. This is for researchers working on near-term quantum ML who need to handle bigger inputs without bigger hardware. A reader running their own QNN experiments will find the MNIST accuracy and the partitioning observation useful to try. It deserves peer review because the central empirical claim is on public data and is stated clearly enough to be checked and extended.

Referee Report

3 major / 2 minor

Summary. The manuscript proposes distributing partitioned input features across multiple small quantum neural networks (QNNs) and generating predictions via an ensemble of their expectation values. This is presented as an alternative to large-circuit approximation that avoids exponential evaluation costs. Empirical results are reported for 10-class classification on the Semeion and MNIST handwritten-digit datasets, with the headline claim that the approach exceeds 96% accuracy on MNIST while reducing per-QNN hardware requirements relative to a single large circuit.

Significance. If the empirical results prove robust under controlled conditions, the partitioned-feature ensemble could provide a practical route to QML on NISQ hardware by sidestepping qubit-count and depth limits. The MNIST result, if substantiated, would be a concrete data point in favor of distributed architectures; however, the absence of training details, statistical controls, and information-retention analysis weakens the immediate impact.

major comments (3)

[Abstract and Numerical Experiments] Abstract and Numerical Experiments section: the central claim of >96% 10-class MNIST accuracy is load-bearing for the contribution, yet the manuscript supplies no description of the training procedure, optimizer, learning-rate schedule, number of shots, or number of independent runs with error bars. Without these, it is impossible to determine whether the reported accuracy reflects the partitioned-ensemble architecture or unstated classical post-processing and hyperparameter choices.
[Abstract and Results] Abstract and Results: the text notes that 'excessive partitioning reduces performance' on Semeion, indicating sensitivity to the (unspecified) partition count and feature-grouping strategy. No ablation study, correlation analysis, or bound on lost inter-feature information is provided, leaving the MNIST result dependent on an unverified assumption that the ensemble preserves sufficient class-separating information.
[Method and Results] Method and Results: no baseline comparisons (classical ML on the same partitioned features, standard single QNN, or random-feature ensembles) or hardware-resource accounting (qubit count, depth, and gate count per small circuit versus a monolithic circuit) are reported, so the claim of 'reduced hardware requirements … compared to a large single quantum neural network' cannot be quantitatively evaluated.

minor comments (2)

[Abstract] Abstract: the phrasing 'exceeding 96% accuracy' is imprecise; a precise statement of the achieved accuracy (e.g., mean and standard deviation across runs) would improve clarity.
[Introduction] Notation: the distinction between the partitioned-feature encoding and standard amplitude or angle encoding is not clearly delineated in the introductory paragraphs, making the novelty relative to prior distributed-QNN work harder to assess.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive comments, which identify key areas where additional details and analyses would strengthen the manuscript. We address each major comment below and will revise the paper to incorporate the requested information and studies.

read point-by-point responses

Referee: Abstract and Numerical Experiments section: the central claim of >96% 10-class MNIST accuracy is load-bearing for the contribution, yet the manuscript supplies no description of the training procedure, optimizer, learning-rate schedule, number of shots, or number of independent runs with error bars. Without these, it is impossible to determine whether the reported accuracy reflects the partitioned-ensemble architecture or unstated classical post-processing and hyperparameter choices.

Authors: We agree these details are necessary for reproducibility and evaluation. In the revised manuscript we will expand the Numerical Experiments section with a complete description of the training procedure (including optimizer, learning-rate schedule, number of shots, and number of independent runs with error bars) so that readers can assess the contribution of the partitioned-ensemble architecture. revision: yes
Referee: Abstract and Results: the text notes that 'excessive partitioning reduces performance' on Semeion, indicating sensitivity to the (unspecified) partition count and feature-grouping strategy. No ablation study, correlation analysis, or bound on lost inter-feature information is provided, leaving the MNIST result dependent on an unverified assumption that the ensemble preserves sufficient class-separating information.

Authors: We acknowledge the value of a systematic study of partitioning effects. The revised version will include an ablation study that varies partition count and feature-grouping strategies on both datasets, together with performance metrics and a discussion of information retention between features. revision: yes
Referee: Method and Results: no baseline comparisons (classical ML on the same partitioned features, standard single QNN, or random-feature ensembles) or hardware-resource accounting (qubit count, depth, and gate count per small circuit versus a monolithic circuit) are reported, so the claim of 'reduced hardware requirements … compared to a large single quantum neural network' cannot be quantitatively evaluated.

Authors: We will add baseline comparisons against classical ML models on the same partitioned features and against single large QNNs (where computationally feasible). We will also include a quantitative hardware-resource comparison (qubit count, circuit depth, and gate count) between the ensemble of small circuits and an equivalent monolithic circuit. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical training results on public datasets

full rationale

The paper reports experimental accuracies from training small QNNs on partitioned MNIST and Semeion features and ensembling expectation values. No equations, derivations, or self-citations are present that reduce the reported performance to fitted inputs by construction or rename known patterns. The method is presented as an empirical architecture choice whose success is measured on held-out test data; the noted performance drop with excessive partitioning on Semeion further indicates the outcome is not guaranteed by the setup itself. This is a standard empirical ML result with no load-bearing self-referential steps.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard quantum circuit assumptions and the empirical effectiveness of feature partitioning; no new entities are postulated. Free parameters include the number of partitions and circuit depth per network, which are chosen to fit the datasets.

free parameters (2)

number of partitions
Chosen to balance performance and hardware constraints; affects whether excessive partitioning reduces accuracy on Semeion.
circuit depth and qubit count per small QNN
Selected to fit near-term hardware limits while enabling training on the given datasets.

axioms (2)

domain assumption Expectation values from parameterized quantum circuits can be trained via classical optimization to perform classification.
Invoked implicitly when stating that small QNNs produce useful predictions that can be ensembled.
domain assumption Partitioned features retain sufficient information for the target classification task.
Required for the claim that the ensemble approach works without exponential overhead.

pith-pipeline@v0.9.0 · 5750 in / 1431 out tokens · 19097 ms · 2026-05-24T05:24:25.820843+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

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Havl´ ıˇ cek, V., C´ orcoles, A.D., Temme, K., Harrow, A.W., Kandala, A., Chow, J.M., Gambetta, J.M.: Supervised learning with quantum-enhanced feature spaces. Nature 567(7747), 209–212 (2019)

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arXiv preprint arXiv:2106.12819 (2021)

Du, Y., Qian, Y., Tao, D.: Accelerating variational quantum algorithms with multiple quantum processors. arXiv preprint arXiv:2106.12819 (2021)

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Marshall, S.C., Gyurik, C., Dunjko, V.: High dimensional quantum machine learning with small quantum computers. Quantum 7, 1078 (2023)

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Bravyi, S., Smith, G., Smolin, J.A.: Trading classical and quantum computational resources. Physical Review X 6(2), 021043 (2016)

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Wang, H., Ding, Y., Gu, J., Li, Z., Lin, Y., Pan, D.Z., Chong, F.T., Han, S.: Quantumnas: Noise-adaptive search for robust quantum circuits. In: The 28th IEEE International Symposium on High-Performance Computer Architecture (HPCA-28) (2022) 10

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